Multi-electrode arrays (MEAs) enable the simultaneous recording of a population of cells. When used on retinal tissue, it is possible to record neural activity from a complete subpopulation of retinal ganglion cells responding to a solid visual angle of a stimulus. This stimulus can be directly controlled and manipulated, enabling one to probe differences in population activity in response to both artificial and natural stimuli.

MEA recordings capture sequences of action potentials, or spikes, generated by individual cells. Within a small time window, the response of a given cell can be treated as a binary event that describes two possible outcomes: the cell fired an action potential (1) or it was silent (0). The response of a population of cells can then be described by a binary firing pattern. At some level, these are the patterns that the brain "sees".

To model population activity, we would like to capture the joint probability distribution of possible firing patterns that could be realized in a population. In retina, this distribution is well described by a minimal pairwise model that captures the mean firing rates of all neurons and covariances between all pairs of neurons. This minimal model is a maximum-entropy model, meaning that it exactly reproduces select observables of the data without introducing any additional structure. We have recently extended these models to include time-dependence, which enables us to study how the distribution of firing patterns changes over time and in response to different stimuli.

Neural responses vary across cells, across stimuli, and across repeated presentations of the same stimulus. Importantly, this trial-dependent variability is correlated across cells. This begs the question as to whether these correlations (termed ``noise correlations'') are noise, or whether they shape the neural code in some meaningful way. In current work, we are designing new theoretical and computational tools to investigate the role of correlated variability in shaping the neural code. In particular, we are investigating whether noise correlations serve a functional purpose, such as shaping the synergy, redundancy, or information content of the code.

While adaptation has been extensively documented at the single-neuron level, much less is known about whether adaptation occurs at the network level. Recent studies predict that such network-level adaptation should occur in response to stimulus variations and should depend on both the correlational structure of the stimulus and the degree of noise in the system. To explore such adaptation, we are working to design new stimulus paradigms for neural recordings. In parallel, we are working to extend theoretical and computational techniques to capture not only single-cell time-dependence, but also time-dependent changes in network couplings.